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November 2018 Large deviations and applications for Markovian Hawkes processes with a large initial intensity
Xuefeng Gao, Lingjiong Zhu
Bernoulli 24(4A): 2875-2905 (November 2018). DOI: 10.3150/17-BEJ948

Abstract

Hawkes process is a class of simple point processes that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applications in finance, insurance, neuroscience, social networks, criminology, seismology, and many other fields. In this paper, we study linear Hawkes process with an exponential kernel in the asymptotic regime where the initial intensity of the Hawkes process is large. We establish large deviations for Hawkes processes in this regime as well as the regime when both the initial intensity and the time are large. We illustrate the strength of our results by discussing the applications to insurance and queueing systems.

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Xuefeng Gao. Lingjiong Zhu. "Large deviations and applications for Markovian Hawkes processes with a large initial intensity." Bernoulli 24 (4A) 2875 - 2905, November 2018. https://doi.org/10.3150/17-BEJ948

Information

Received: 1 April 2016; Revised: 1 February 2017; Published: November 2018
First available in Project Euclid: 26 March 2018

zbMATH: 06853268
MathSciNet: MR3779705
Digital Object Identifier: 10.3150/17-BEJ948

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

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Vol.24 • No. 4A • November 2018
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